Three-dimensional simulations of non-stationary accretion by remnant black holes of compact object mergers

¹ School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland, UK e-mail: [S.Setiawan;M.Ruffert]@ed.ac.uk
² Max-Planck-Institut für Astrophysik, Postfach 1317, 85741 Garching, Germany e-mail: thj@mpa-garching.mpg.de

Received: 12 September 2005
Accepted: 21 July 2006

Abstract

By means of three-dimensional hydrodynamic simulations with an Eulerian PPM code we investigate the time-dependent evolution and properties of accretion tori around nonrotating and rotating stellar-mass black holes, using a pseudo-Newtonian (Paczyński & Wiita or Artemova-Björnsson-Novikov) potential to approximate the effects of general relativity. The simulations are performed with three nested Cartesian grids to ensure sufficient resolution near the central black hole on the one hand and a large computational volume on the other. The black hole and torus are considered as the remnant of a binary neutron star or neutron-star black-hole merger. Referring to results from previous hydrodynamical simulations of such events, we assume the initial configurations to consist of a black hole with a mass of about 4 girded by a toroidal accretion disk with a mass in the range from about 0.01  to 0.2 . We simulate the torus evolution without and with physical shear viscosity, employing a simple α-model for the gas viscosity. As in our previous work on merging neutron star binaries and neutron star/black hole binaries, we use the equation of state of Lattimer and Swesty. The energy loss and lepton number change due to neutrino emission from the hot torus are treated by a neutrino-trapping scheme. The energy deposition by neutrino-antineutrino annihilation around the disk is evaluated in a post-processing step. The time-dependent efficiency of converting gravitational energy to neutrinos, expressed by the ratio of neutrino luminosity to accretion rate of rest-mass energy, can reach maximum values of up to about 10%. The corresponding efficiency of converting neutrino energy into a pair-photon fireball by neutrino annihilation peaks at values of several percent. Interestingly, we find that the rate of neutrino-antineutrino annihilation decays with time much less steeply than the total neutrino luminosity does with the decreasing gas mass of the torus, because the ongoing protonization of the initially neutron-rich disk matter leads to a rather stable product of neutrino and antineutrino luminosities. The neutrino luminosity and total energy release of the torus increase steeply with higher viscosity, larger torus mass, and larger black hole spin in corotation with the disk, in particular when the spin parameter is . The latter dependence is moderated in case of a high disk viscosity. For rotation rates as expected for post-merger black holes () and reasonable values of the alpha viscosity of the torus (), torus masses in the investigated range can release sufficient energy in neutrinos to account for the energetics of the well-localized short gamma-ray bursts recently detected by Hete and Swift, if collimation of the ultrarelativistic outflows into about 1% of the sky is invoked, as predicted by recent hydrodynamic jet simulations.